The serial test for pseudo-random numbers generated by the linear congruential method

1985 ◽  
Vol 46 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Harald Niederreiter
Keyword(s):  
Random Numbers ◽  
Serial Test ◽  
Congruential Method ◽  
Linear Congruential

Penerapan Linear Congruential Method pada Aplikasi Ujian Berbantuan Komputer

2018 ◽  
Vol 1 ◽  
Author(s):  
Puji Rahayu Ningsih ◽  
Muhamad Afif Effindi
Keyword(s):  
Learning Outcomes ◽  
Student Learning Outcomes ◽  
Random Numbers ◽  
Pseudorandom Number Generator ◽  
Computer Based ◽  
Congruential Method ◽  
Written Test ◽  
Linear Congruential ◽  
Bloom Taxonomy ◽  
Randomization Method

In order to obtain information regarding student learning outcomes, the test is one way to go. Both test orally and written test. Along with the development of technology, the current written test is no longer done on paper but done using computer media. Computer-based test is one of the exam types applied in the National Exam and have been implemented in some schools in Indonesia. In this exam, it is possible for students to work on different packages of problems with their colleagues on the side. This is possible because of the problem randomization method. Nevertheless, it should be tested whether in the randomization of the problem has noticed the sequence of occurrences of questions which is still pay attention to the sequence as Bloom Taxonomy. This study focuses on applying the Linear Congruential Method, in order to generate a random problem from the database. The method called Pseudorandom Number Generator. In practice, the Linear Congruential Method method use variables a, c, and m as inputs for the occurrence of random numbers simultaneously. In this study, the numbers a and m are set first. While the variable c obtained from random numbers generated in the previous stage. The result of this research is the computer-based test which applies for random numbers.

scholarly journals Generator of PRN's on the norm group

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 26-39
Author(s):  
P. Fugelo ◽  
S. Varbanets
Keyword(s):  
Prime Number ◽  
Quadratic Field ◽  
Exponential Sum ◽  
Random Numbers ◽  
Gaussian Integers ◽  
New Family ◽  
Serial Test ◽  
Polynomial Representations ◽  
Modulo P ◽  
Norm Group

Let $p$ be a prime number, $d\in\mathds{N}$, $\left(\frac{-d}{p}\right)=-1$, $m>2$, and let $E_m$ denotes the set of of residue classes modulo $p^m$ over the ring of Gaussian integers in imaginary quadratic field $\mathds{Q}(\sqrt{-d})$ with norms which are congruented with 1 modulo $p^m$. In present paper we establish the polynomial representations for real and imagimary parts of the powers of generating element $u+iv\sqrt{d}$ of the cyclic group $E_m$. These representations permit to deduce the ``rooted bounds'' for the exponential sum in Turan-Erd\"{o}s-Koksma inequality. The new family of the sequences of pseudo-random numbers that passes the serial test on pseudorandomness was being buit.

Feistel-inspired scrambling improves the quality of linear congruential generators

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Asia Aljahdali ◽  
Michael Mascagni
Keyword(s):  
Randomized Algorithms ◽  
Statistical Properties ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Linear Congruential Generators ◽  
Pseudorandom Number Generation ◽  
Linear Congruential ◽  
Test Suites

AbstractGenerating pseudorandom numbers is a prerequisite for many areas including Monte Carlo simulation and randomized algorithms. The performance of pseudorandom number generators (PRNGs) depends on the quality of the generated random sequences. They must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers such as those from the TestU01 library, the DIEHARD test suite, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. This paper presents a new pseudorandom number generation scheme that produces pseudorandom sequences with good statistical properties via a scrambling procedure motivated by cryptographic transformations. We will specifically apply this to a popular set of PRNGs called the Linear Congruential generators (LGCs). The scrambling technique is based on a simplified version of a Feistel network. The proposed method seeks to improve the quality of the LCGs output stream. We show that this Feistel-inspired scrambling technique breaks up the regularities that are known to exist in LCGs. The Feistel-inspired scrambling technique is modular, and can be applied to any 64-bit PRNG, and so we believe that it can serve as an inexpensive model for a scrambler that can be used with most PRNGs via post-processing.

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